few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Make geometric constructions.

Experiment with transformations in the plane.

Visualize relationships between two-dimensional and three-dimensional objects.

Apply geometric concepts in modeling situations.

Prove geometric theorems.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Prove theorems involving similarity.

Find arc lengths and areas of sectors of circles.

Understand congruence in terms of rigid motions.

Reason with shapes and their attributes.

Define trigonometric ratios and solve problems involving right triangles.

Classify two-dimensional figures into categories based on their properties.

Translate between the geometric description and the equation for a conic section.

Apply trigonometry to general triangles.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Solve real-world and mathematical problems involving area, surface area, and volume.

Explain volume formulas and use them to solve problems.

Understand and apply theorems about circles.

Understand and apply the Pythagorean Theorem.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Use coordinates to prove simple geometric theorems algebraically.

Analyze, compare, create, and compose shapes.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand similarity in terms of similarity transformations.
problem_activity: Narrative
The purpose of this activity is for students to use informal language and the structure of the coordinate grid to describe a given shape. Some questions may be about properties of the shape rather than its location. For example, “Is the rectangle wider than it is tall?” is a question that eliminates many shapes. As the number of shapes decreases, the location will become more important and the features of the coordinate grid will play a larger role. The synthesis gives students an opportunity to consider how the numbers in the coordinate grid can be useful to accurately describe the attributes, location, and orientation of a given shape (MP6).
Launch
Groups of 2
Activity
5 minutes: partner work time
Monitor for students who:
reference the structure of the grid in their questions
reference the numbers on the horizontal and vertical axes in their questions
use gestures to indicate horizontal or vertical gridlines
use the words horizontal or vertical
Student Facing
Play a round of Guess Which One.
Sit next to your partner.
Partner A:
Mentally choose a shape card without indicating which shape card you chose.
Partner B:
Ask yes or no questions to determine which shape card partner A has chosen.
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
E
[IMG]
F
[IMG]
G
[IMG]
H
[IMG]
I
[IMG]
J
[IMG]
K
[IMG]
L
[IMG]
Switch roles and play another round of Guess Which One.
Diego and Kiran were playing a round of Guess Which One. These are the last two shapes. What question can Kiran ask to determine which shape is the one that Diego picked?
[IMG]
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not reference the grid lines or numbers when asking questions, refer to the display from the first activity and ask, “Which words can you use to help you figure out which shape your partner chose?”
Activity Synthesis
Ask previously identified students to share their reasoning.
“How do the numbers help us locate shapes on the grid?” (I could use them to describe the lines and the points. I could also use numbers to describe the location of the shape: “Go up three. Go over 5.”)
“The gridlines with numbers on them are called
axes
. The coordinate grid has a
horizontal axis
and a
vertical axis
.”


correct_option_index: 20